Testing models for penetrant diffusion in glassy polymers

Data from forced-Rayleigh scattering studies of diffusion coefficients for camphorquinone and diacetyl in poly(methyl methacrylate) in the glassy regime were used to test two models for this quantity. Free-volume theory with the parameter-choice method suggested by Vrentas and co-workers [Vrentas JS, Vrentas CM. Eur Polym J 1998;34:797] predicts an activation energy (ca. 250 kJ mol−1) which is a factor of about 2 greater than experiment, and a pre-exponential factor which is several orders of magnitude too large: thus this model underestimates experimental diffusion coefficients by many orders of magnitude at the temperatures studied. This is ascribed to free-volume theory being inapplicable to the actual mechanism for penetrant diffusion in glassy polymers: simulations suggest that this occurs instead by occasional jumps between cavities through the opening of a “neck”. This jump mechanism is explicitly taken into account by the second model tested here [Gray-Weale AA, Henchman RH, Gilbert RG, Greenfield ML, Theodorou DN. Macromolecules 1997;30:7296]. Although this model successfully predicts diffusion coefficients of small nonpolar penetrants, it is found to greatly overestimate observed diffusion coefficients in the present system, perhaps because it underestimates the attractive potentials between the penetrant and the polymer matrix and/or breakdown of the modelʹs assumption of linear elastic deformation for relatively large penetrants.